This invention is an improvement over the Autolocking Self-Piercing Rivet disclosed in my co-pending application Ser. No. 906,479 filed May 17, 1978 in that it provides for a riveted fastening of sheet materials wherein the ends of the rivet are flush with the surfaces of the fastened materials. Headless riveting itself is not new, as indicated by U.S. Pat. Nos. 3,130,489 and 3,729,804. However, in each of these cases, the lower of the pieces being fastened together must be pre-punched to provide an opening for the fastening element and in no case is the fastening means flush with the surfaces of the finished work.